src/v8/test/mjsunit/es6/math-expm1.js

// Copyright 2014 the V8 project authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

// Flags: --no-fast-math

assertTrue(isNaN(Math.expm1(NaN)));
assertTrue(isNaN(Math.expm1(function() {})));
assertTrue(isNaN(Math.expm1({ toString: function() { return NaN; } })));
assertTrue(isNaN(Math.expm1({ valueOf: function() { return "abc"; } })));
assertEquals(Infinity, 1/Math.expm1(0));
assertEquals(-Infinity, 1/Math.expm1(-0));
assertEquals(Infinity, Math.expm1(Infinity));
assertEquals(-1, Math.expm1(-Infinity));


// Sanity check:
// Math.expm1(x) stays reasonably close to Math.exp(x) - 1 for large values.
for (var x = 1; x < 700; x += 0.25) {
  var expected = Math.exp(x) - 1;
  assertEqualsDelta(expected, Math.expm1(x), expected * 1E-15);
  expected = Math.exp(-x) - 1;
  assertEqualsDelta(expected, Math.expm1(-x), -expected * 1E-15);
}

// Approximation for values close to 0:
// Use six terms of Taylor expansion at 0 for exp(x) as test expectation:
// exp(x) - 1 == exp(0) + exp(0) * x + x * x / 2 + ... - 1
//            == x + x * x / 2 + x * x * x / 6 + ...
function expm1(x) {
  return x * (1 + x * (1/2 + x * (
              1/6 + x * (1/24 + x * (
              1/120 + x * (1/720 + x * (
              1/5040 + x * (1/40320 + x*(
              1/362880 + x * (1/3628800))))))))));
}

// Sanity check:
// Math.expm1(x) stays reasonabliy close to the Taylor series for small values.
for (var x = 1E-1; x > 1E-300; x *= 0.8) {
  var expected = expm1(x);
  assertEqualsDelta(expected, Math.expm1(x), expected * 1E-15);
}


// Tests related to the fdlibm implementation.
// Test overflow.
assertEquals(Infinity, Math.expm1(709.8));
// Test largest double value.
assertEquals(Infinity, Math.exp(1.7976931348623157e308));
// Cover various code paths.
assertEquals(-1, Math.expm1(-56 * Math.LN2));
assertEquals(-1, Math.expm1(-50));
// Test most negative double value.
assertEquals(-1, Math.expm1(-1.7976931348623157e308));
// Test argument reduction.
// Cases for 0.5*log(2) < |x| < 1.5*log(2).
assertEquals(Math.E - 1, Math.expm1(1));
assertEquals(1/Math.E - 1, Math.expm1(-1));
// Cases for 1.5*log(2) < |x|.
assertEquals(6.38905609893065, Math.expm1(2));
assertEquals(-0.8646647167633873, Math.expm1(-2));
// Cases where Math.expm1(x) = x.
assertEquals(0, Math.expm1(0));
assertEquals(Math.pow(2,-55), Math.expm1(Math.pow(2,-55)));
// Tests for the case where argument reduction has x in the primary range.
// Test branch for k = 0.
assertEquals(0.18920711500272105, Math.expm1(0.25 * Math.LN2));
// Test branch for k = -1.
assertEquals(-0.5, Math.expm1(-Math.LN2));
// Test branch for k = 1.
assertEquals(1, Math.expm1(Math.LN2));
// Test branch for k <= -2 || k > 56. k = -3.
assertEquals(1.4411518807585582e17, Math.expm1(57 * Math.LN2));
// Test last branch for k < 20, k = 19.
assertEquals(524286.99999999994, Math.expm1(19 * Math.LN2));
// Test the else branch, k = 20.
assertEquals(1048575, Math.expm1(20 * Math.LN2));